value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Evaluate the inverse function , Question: a. What is the inverse of f (...

Question: a. What is the inverse of f (x)? b. Graph the inverse function from part (a). c. Rewrite the inverse function from part (a) in exponential form. d. Evaluate

Sketch the direction field for the differential equation, Sketch the direct...

Sketch the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Find out how the solutions behave as t → ∞ and

The rank correlation coefficient (r), The Rank Correlation Coefficient (R) ...

The Rank Correlation Coefficient (R) Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among tw

Triangle Treat, Triangle Treat is the page name. I don''t know the answer f...

Triangle Treat is the page name. I don''t know the answer for it, can someone give it to me?

Profits and loss, what does 1000/q in the ATC equation represent economical...

what does 1000/q in the ATC equation represent economically?

Factor , #Mai iss 3 years younger than twice the age of her brother . If b ...

#Mai iss 3 years younger than twice the age of her brother . If b represents the age of Mai''s brother .which expression below represents Mai''s age 2-3b 3-2b 2b-3 3b-2 2-3b 3-2b q

Calculate the width of the river, A surveyor is hired to calculate the widt...

A surveyor is hired to calculate the width of a river. Using the example provided, Calculate the width of the river. a. 48 ft b. 8 ft c. 35 ft d. 75 ft

#perimeter, what are the formulas in finding the perimeter of a plane figur...

what are the formulas in finding the perimeter of a plane figure?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd